The maximum of the smallest maximal coordinate of the minimum vectors in 6-lattices equals 1

A. Végh

Abstract: This paper is related to the question of \'A. G. Horv\'ath \cite{agh1}: How to find a basis of any $n$-lattice in $ \mathbb{E}^n$ such that the maximal coordinate belonging to the minima of this lattice are ``small as possible. We prove that in the 6-dimensional case, in every lattice there exists a basis for which all the coordinates of the minima are $-1,0,1$.